The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  X  1  X X+2  1  0  2  1  1  1  1  1  1  0  1 X+2 X+2  1 X+2  1  X  2  1  1  1
 0  1  0  1  0 X+3  1  X X+2  1  X  1 X+3  1  1  1  2  1  0 X+3 X+1 X+3  0  2  1  0  X  2 X+2  0  3  2  X  3 X+3  0
 0  0  1  1  1  0  1  1  X  0 X+1  X  1 X+1  2  0  1  3  3  0 X+3  3  0  1 X+3 X+1  1  1 X+2  1 X+1  2  1  0 X+3  0
 0  0  0  X  0 X+2  2  X  2  2 X+2 X+2  2 X+2  X X+2  2 X+2  X  2  2 X+2 X+2  X  X  0 X+2 X+2  X  2  2 X+2  0  X X+2  0
 0  0  0  0  X  0  2 X+2 X+2  X  2 X+2  0  0  2 X+2 X+2  X  X  2  0  X  X  X  2 X+2  2  0  2  X  2  2  0  2  2  0
 0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  0  2  0  0  0  2  0  2  2  0  2  2  2  0  0  0  2  2  2  0  0

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+48x^28+178x^29+400x^30+652x^31+941x^32+1328x^33+1664x^34+1900x^35+2045x^36+2002x^37+1802x^38+1368x^39+882x^40+582x^41+276x^42+140x^43+110x^44+36x^45+18x^46+4x^47+4x^48+2x^49+1x^52

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 5.5 seconds.